Optimal design and analysis for two-phase experiments with random block and treatment effects

• Applicant: Professor Dr. Hans-Peter Piepho
• Subject Area: Plant Cultivation, Plant Nutrition, Agricultural Technology ; Plant Breeding and Plant Pathology
• Term: from 2016 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 317047028

• Final Report Year: 2023

Final Report Abstract

Many agricultural experiments have more than one phase. For example, plant breeding experiments involve a field phase, in which different genotypes are grown, and a lab phase, in which plot samples are analysed for various quality traits such as baking quality in wheat. Blocking in field experiments has been a standard procedure for about a century but few researchers use an efficient statistical design also in the lab phase. In the simplest case the block structure used in the first phase can be fully transferred to the second phase. Often, however, the block sizes differ between phases, in which case the design problem becomes non-trivial. This project extended our previous work on optimal design of two-phase experiments to the case where blocks or treatments or both are considered as random. To this end, we defined Bayesian criteria for A-optimality. A further challenge is the efficient computation of the update for the treatment information matrix during numerical design search. For this problem, we developed efficient update formulae. The algorithmic framework was implemented in a Julia package. Several applications were published where this new framework was used to search efficient designs with fixed or random block and treatment effects.

Publications

• Augmented quasi-sudoku designs in field trials. Computational Statistics & Data Analysis, 150 (2020, 10), 106988.
  Vo-Thanh, Nha & Piepho, Hans-Peter
  
• Die Gleitmethode nach Mitscherlich und was sie mit Geostatistik zu tun hat. Journal für Kulturpflanzen 72, 527-540
  Piepho, H.P., Vo-Thanh, N.
  
• Generating experimental designs for estimation of genetically related treatment effects using SAS. Agronomy Journal, 112(5), 3929-3940.
  Piepho, Hans‐Peter; Vo‐Thanh, Nha & Tobias, Randy
  
• Generating row–column field experimental designs with good neighbour balance and even distribution of treatment replications. Journal of Agronomy and Crop Science, 207(4), 745-753.
  Piepho, Hans‐Peter; Williams, Emlyn R. & Michel, Volker
  
• Bayesian A-optimal two-phase designs with a single blocking factor in each phase. Statistics and Computing, 33(1).
  Vo-Thanh, Nha & Piepho, Hans-Peter
  
• Single-parent expression complementation contributes to phenotypic heterosis in maize hybrids. Plant Physiology, 189(3), 1625-1638.
  Baldauf, Jutta A; Liu, Meiling; Vedder, Lucia; Yu, Peng; Piepho, Hans-Peter; Schoof, Heiko; Nettleton, Dan & Hochholdinger, Frank
  
• Generating Designs for Comparative Experiments with Two Blocking Factors. Biometrics, 79(4), 3574-3585.
  Vo-Thanh, Nha & Piepho, Hans-Peter